More of My Ignorance on Display - Calling all Cooks

That's called a garlic press.  I personally don't like using them because it wastes so much of the clove.  (By the way, the whole "lump" of garlic is called a bulb. lol)

Here's a great YouTube video showing you the proper way to mince garlic. 
http://www.youtube.com/watch?v=hOTVQIBQDOI

 Usually in my recipe directions I call for adding the garlic after you sautee the onions and veggies, but some posts may be before I learned that little gem of information. 

Also roasting garlic is divine if you are ever making a soup. You simply peel it, toss it in a little olive oil and roast it on 400 for about 10-ish minutes. It gets so sweet!

foodnetwork.com

i always buy the stuff that is already minced up in a jar...much easier for me, and the bulbs of garlic alwasy seemd to go bad before i could use them all..so this jar works the best for me...and if you have a chance, watch the rachel ray show, she shows great ways to measure out the spices and herbs...she doesnt use measure cups..but the palm of her hand....and how many turns of the pan for her olive oil, no measureing cups...
i have learned lots from her down to earth stlye of cooking...
good luck on your endeavor to learn to cook...
debby

I forgot to answer your chopping vs. dicing question.  Chopping, say an onion, will leave you with different sized pieces.  When they're cooked or sauteed, they will have different textures as the smaller pieces will cook quicker and the larger pieces will not.

When you dice, again, say an onion, the pieces are uniform which will give you even texture when they're cooked.  In my opinion, dicing is prettier, so if I'm making a fresh salsa I want that look over chopped.

 Now see that's where having my mom came in handy. I was in charge of prepping veggies from age 10 on. I think you'd call my chop a dice. 

Because of my mom I also know how to julienne veggies and ribbon them by hand.

 On the subject of garlic (Gar Licca from the Latin, "Food of the Lone Hero") (not):
The easiest way to peel it is to smash* a clove with the flat of your big knife. The skin pops right off. Then you just chop it up with the same knife.
I've no use for those garlic presses. I asked for one for Christmas once and used it twice. Messy and wasteful.

*Your smash may differ from mine. 

I OWN a garlic press but have never used it. I, too, smash.

I also am vehemently against jarred garlic if I can avoid it. I use it enough where if I buy one clove it goes in pretty good time.